`E_(1),E_(2)` and `E_(3)` are the emfs of the following three galvanic cells respectively.
(i)`Zn_((s))|Zn^(2+)(0.1M)||Cu^(2+)(1M)|Cu_((s))`
(ii)`Zn_((s))|Zn^(2+)(1M)||Cu^(2+)(1M)|Cu_((s))`
(iii)`Zn_((s))|Zn^(2+)(1M)||Cu^(2+)(0.1M)|Cu_((s))`
Which one of the following is true?

Options

A. `E_(2)gtE_(1)gtE_(3)`
B. `E_(1)gtE_(2)gtE_(3)`
C. `E_(3)gtE_(1)gtE_(2)`
D. `E_(3)gtE_(2)gtE_(1)`

Answer

B

Explanation

`E_(cell)=E_("ox")+E_(red)-(0.591)/(n)log[(Zn^(2+))/(Cu^(2+))]`
`E_(red)^(@)` for `Cu^(2)//Cu=0.35V`
`E_("ox")^(@)` for `Zn//Zn^(2+)`=0.76 V
`therefore E_(cell)^(@)=E_(red)^(@)+E_("ox")^(@)=0.35+0.76=1.11V`
`Zn_(s)|Zn^(2+)(0.1M)|Cu^(2+)(1M)|CU_(s)`,`E_(1)`
`E_(cell)=E_(cell)^(@)-(0.0591)/(n)log[(Zn^(2+))/(Cu^(2+))]`
`=1.11-(0.591)/(2)log(0.1)/(1)=1.11+(0.591)/(2)toE_(1)`
(ii)For`Zn_(s)|Zn^(2+)(1M)|Cu^(2+)(1M)|Cu_(s)`
`E_(cell)=1.11-(0.591)/(2)log(1)/(1)`
`E_(cell)=1.11toE_(2)`
(iii)Fo`Zn_(s)|Zn^(2+)(1M)||Cu^(2+)(1M)|Cu_(s)`
`E_(cell)=1.11-(0.0591)/(2)log(1)/(0.1)=1.11-(0.0591)/(2)toE_(3)`
`therefore E_(1)gtE_(2)gtE_(3)`.